Tens of thousands of NSW school students have started the school year after undergoing the first of many rapid antigen tests.

NSW Premier Dominic Perrottet said there would be bumps along the way and “it won’t be all smooth-sailing” but it was important for children to get back to classrooms.

“I know that many parents are anxious … but the alternative is to have schools closed and … it’s not the outcome that’s best for our kids,” he said.

“There’s nothing more important than having our kids back in the classroom,” he said on Tuesday at Sydney’s Ultimo Public school.

Catholic school children returned to classrooms in NSW on Monday but most state pupils started on Tuesday, testing the government’s new COVID-19 protocols for face-to-face teaching amid the Omicron outbreak.

Teachers and students are required to test for COVID-19 twice weekly, year groups will be segregated, ventilation has been improved, children have been getting vaccinated and high school students and teachers must wear masks.

Education Minister Sarah Mitchell acknowledged that adding a RAT to a family’s morning routine was a big ask but said it was important to keep children, their classmates and teachers safe.

“I’ve had such overwhelmingly positive feedback not just from parents but also from teachers and principals,” she said.

Mr Perrottet also announced that from Monday, the state’s private hospitals, and public hospitals in regional and rural areas, would begin a staged return to resume non-urgent elective surgery.

“We thought that … we could bring that back in mid-February but we’ve been able to bring that forward,” he said.

“I think [that] is a testament to the strength of our health system.”

NSW Health reported 12,818 cases of COVID and 30 deaths in the 24 hours to 8pm on Monday.

Chief health officer Dr Kerry Chant said a man in his 30s who was double vaccinated and had no significant underlying health conditions had died.

The remaining deaths were a person in their 50s, five people in their 70s, 19 in their 80s and four in their 90s.

“Five of the people who died had received three doses of the COVID vaccine, 19 people had received two doses and six were not vaccinated,” Dr Chant said.

There are 2749 people with COVID in hospital in NSW, 184 of them in ICU and and 70 are ventilated.

More than 78 per cent of students aged 12-15 have had two doses of a COVID-19 vaccine while nearly 40 per cent of children aged 5-11 have had one dose.

Of the eligible population, 44.7 per cent of people in NSW have had a booster shot.

“I would love that pace to pick up,” Dr Chant said.

Health Minister Brad Hazzard confirmed some regional and rural public hospitals would have the capacity to resume overnight non-urgent elective surgeries from Monday, while metropolitan public hospitals would remain focused on caring for COVID-19 patients.

“Our hospitals remain under pressure due to COVID-19 so only our public hospitals that are in a position to resume non-urgent elective surgeries without compromising their ability to care for COVID-19 patients and patients with other medical conditions will do so,” he said.

Bringing back the full range of elective surgery in metropolitan hospitals would take longer.

“That would depend entirely on keeping those numbers down and that depends entirely on us all … getting a booster,” he said.

-AAP